1. The Problem Formulation
A signal driving a loudspeaker must remain below a certain limit. If the signal is too high, the loudspeaker will generate nonlinear distortions or will be irreparably damaged. One cause of this nonlinear distortion or damage is an excess vibration displacement of a diaphragm-coil assembly of the loudspeaker. To prevent nonlinear distortion or damage, this displacement must be limited.
Displacement limiting can be implemented by continuously monitoring the displacement by a suitable vibration sensor, and attenuating the input signal if the monitored displacement is larger than the known safe limit. This approach is generally unpractical due to the expensive equipment required for measuring the vibration displacement. Thus some type of a predictive, model-based approach is needed.
2. Prior Art Solutions
The prior art of the displacement limiting can be put into three categories:                1. Variable cut-off frequency filters driven by displacement predictors.        2. Feedback loop attenuators.        3. Multi-frequency band dynamic range controllers.        
The prior art in the first category has the longest history. The first such system was disclosed in U.S. Pat. No. 4,113,983, “Input Filtering Apparatus for Loudspeakers”, by P. F. Steel. Further refinements were disclosed in U.S. Pat. No. 4,327,250, “Dynamic Speaker Equalizer”, by D. R. von Recklinghausen and in U.S. Pat. No. 5,481,617, “Loudspeaker Arrangement with Frequency Dependent Amplitude Regulations” by E. Bjerre. The essence of the prior art in the first category, utilizing a variable high pass filter with a feedback control for said displacement limiting, is shown in FIG. 1a. 
In this category of loudspeaker protection systems (as shown in FIG. 1a), a high-pass filter 12 of a signal processor 10 filters the input electro-acoustical signal 22. Then a filtered output signal 24 of said high-pass filter 12 is sent to a loudspeaker 20 (typically, through a power amplifier 18) and also fed to a feedback displacement predictor block 14. If the value of the displacement exceeds some predefined threshold value, a feedback displacement prediction signal 26 from the block 14 indicated that and a cut-off frequency of the high-pass filter 12 is increased based on the feedback frequency parameter signal 28 provided to the high-pass filter 12 by a feedback parameter calculator 16 in response to said feedback displacement prediction signal 26. By increasing the cut-off frequency of the high-pass filter 12, lower frequencies in the input signal, which generally are the cause of the excess displacement, are attenuated, and the excess displacement is thereby prevented.
The prior art in the first category has several difficulties. The high-pass filter 12 and the feedback displacement predictor block 14 have finite reaction times; these finite reaction times prevent the displacement predictor block 14 from reacting with sufficient speed to fast transients. Bjerre presented a solution to this problem in U.S. Pat. No. 5,481,617 at the expense of significantly complicating the implementation of the displacement limiting system. An additional problem comes from the fact that the acoustic response of the loudspeaker naturally has a high-pass response characteristic: adding an additional high-pass filter in the signal chain in the signal processor 10 increases the order of the low-frequency roll-off. This can be corrected by adding to the signal processor a low-frequency boosting filter after the high-pass filter, as was disclosed by Steel in U.S. Pat. No. 4,113,983. However, this further complicates the implementation of the signal processing.
Prior art in the second category was disclosed in U.S. Pat. No. 5,577,126, “Overload Protection Circuit for Transducers”, by W. Klippel. FIG. 1b shows the essence of a loudspeaker protection system describing this category. The output of the displacement predictor is fed-back into the input signal, according to a feedback parameter κ, calculated by a threshold calculator. This category of the vibration displacement protection is simpler than the first category system described above, in that it does not require a separate high-pass filter.
Prior art in the second category can be effective for the vibration displacement limiting. However, the feedback loop has an irregular behaviour around a threshold value, due to a modification of the loudspeaker's Q-factor, and an amplification at low frequencies. These effects can cause subjectively objectionable artifacts. In the above-mentioned U.S. Pat. No. 5,577,126, Klippel describes one solution to this problem: the attenuation of the signal processor is somewhat better behaved if the pure feedback signal path 16 is differentiated, as shown in FIG. 3 of U.S. Pat. No. 5,577,126. However, this causes significant and unnecessary attenuation of the higher frequency band. Therefore, signals that are not responsible for the excess displacement are likely to be attenuated, degrading the performance of the loudspeaker system.
Prior art in the third category was disclosed in WO Patent Application No. PCT/EP00/05962 (International Publication Number WO 01/03466 A2), “Loudspeaker Protection System Having Frequency Band Selective Audio Power Control”, by R. Aarts. FIG. 1c shows the essence of the third category loudspeaker protection system. The input signal is divided into N frequency bands by a bank of band-pass filters. The signal level in the nth frequency band is modified by a variable gain gn. The signals in the N frequency bands are summed together, and sent to the power amplifier and loudspeaker. An information processor monitors the signal level in each frequency band, as modified by each of the variable gains g1, g2, . . . gn. The information processor modifies the variable gains g1, g2, . . . gn in such a way as to prevent the excess displacement in the loudspeaker. The advantage of the third category approach is that the signal is attenuated in only that frequency band that is likely to cause the excess loudspeaker diaphragm-coil displacement. The remaining frequency bands are unaffected, thereby minimizing the effects of the displacement limiting on the complete audio signal.
The disadvantage of the third category displacement limiter is that there are no formal rules describing how the information processor should operate. Specifically, no formal methods are available for describing how the information processor should modify the gains gn so as to prevent the output signal from driving the loudspeaker's diaphragm-coil assembly to the excess displacement. The information processor can only be designed and tuned heuristically, i.e., by a trial-and-error. This generally leads to a long development time and an unpredictable performance.